Thursday, June 17, 2021

Traveller and Warhammer 40k

Another product of a discussion with my father.

We played Dark Heresy (1e) together for a short campaign or two.  We more or less agree that it's a fun premise for a game, but a lousy system.

Meanwhile, Traveller is a pretty decent system, but it's hobbled by the fact that its implicit setting and expected conventions of play are unfamiliar.  There is no Appendix N of fiction in the Classic Traveller books, unfortunately.  So people misuse it for Firefly when it was meant for Space Viking and Dumarest (or so I'm told).  About the closest I've read, works of that era that get at the "Imperial Science Fiction" feel, might be Dune or Foundation.

But it's not quite true that Imperial Science Fiction has no heirs.  Warhammer 40k is also Imperial Science Fiction of a sort, though a deeply pessimistic lens.  You have a sprawling, strongly human-centric empire with subsector and planetary governments who are only loosely under the thumb of central power - just like Traveller.  You have faster than light travel which is slow, unreliable, and leaves ships isolated from each other for the duration, just like Traveller.  FTL communication exists, and it's faster than FTL travel, but still not great in either.  All three of these are features which permit characters out on the fringes much more autonomy than would otherwise be expected.  Psionics are rare, dangerous, and stigmatized, much more so than in Traveller.  How many science fiction settings have psionics at all, nevermind agreeing on the general attitude towards them?  Ship ownership by private individuals, the Rogue Traders, is rare and inherited, versus ship ownership being rare and just extraordinarily expensive in Traveller (I guess you could do multi-generation-term inherited starship loans...).  Powered armor (and the skills to use it) is also very rare and expensive in both, while both also have very heterogeneous mixes of tracked, wheeled, and grav vehicles and both energy weapons and slugthrowers in common use.  The emphasis on melee combat is surprisingly high for science fiction in both - "cutlass" is a legitimate weapon choice in both.  And the position of anti-aging treatments in both settings has some similarities; they exist, but they're rare, expensive, for the rich and powerful, probably not for your character.

I recall hearing tell that Warhammer 40k's setting had its origins in Traveller's universe, but filtered through a British black comedy 2300 AD / Judge Dredd lens.  And the more I think about it the more right it seems.

So the natural conclusion is that Traveller is probably a really darn good system for running Warhammer 40k RPGs; almost certainly better than the baroque percentile monstrosities that have been churned out in the last ten years.  And if you want modern gamers to understand Traveller's default assumptions, you could do a lot worse than describing the setting as a lot like Warhammer 40k, but less grimdark, with all the craziness dialed down to like a 3.  Yes there are space marines in powered armor and they'll probably ruin your day if you try to fight them, but under the armor they're just well-trained dudes, not centuries-old super-soldiers.  Yes the planet is a feudal technocracy and it's sort of like it's run by the Mechanicus but they're not as culty and not as cyborg.

The real question is whether you'd use Striker or the actual WH40k wargame rules to resolve small mass combats.

And hey, nothing says "To be a man in such times is to be one amongst untold billions.  It is to live in the cruelest and most bloody regime imaginable" quite like death in chargen.

Thursday, June 10, 2021

Winning at D&D, Domains as Endgame

I've been playing Grim Dawn lately, in addition to a little Deep Rock Galactic.  I'm getting up towards "endgame" in both of them.  I had never really considered "endgame" in the context of RPG-like games with leveling / progression systems (as opposed to, say, grand strategy games where "endgame" is when your strategy has come to fruition, your position is secure, and you get to coast to victory).  The way it seems to be used in Grim Dawn and DRG is that your progression stops or slows, but difficult and very time-consuming content remains, to interact with optionally.

Looking at Basic D&D through this lens of CRPG terminology, it seems like name level (9th-10th) is almost a soft-cap.  The XP to level changes from exponential to linear (with a steep slope), the rate of HP gain is halved, you've gotten most of the attack throw and save improvement that you're going to get, and you start getting access to new, expensive content on long time-scales: domains.

There are problems with this model, mostly around MUs getting access to 6th level spells at 11th, and some thief skills still don't get up into the 90+% range until 12th - but switching from 5% improvements to 1% or 2% improvements is a very soft-cap "diminishing returns" change of progression structure.  I don't think I would mind a variation that made this more explicit, by making 6th level MU spells ritual magic, and compressing thief skill advancement so that eg Hide in Shadows did get up around 85% by 9th level and then improve by about 2% per level thereafter.

Incidentally, having very-fine-grained progress on thief skills post-9th level might be the best argument I've ever considered of for using percentile thief skills rather than d20 or d6.

I think it would be reasonable to think of making it into the 9th-11th level range as "winning" at D&D.  You've made it over the hump and fulfilled the default goal of accumulating personal power; further efforts to accumulate personal power will be slow going.  But now you have enough power to pick your own goals.  Or you could just retire to your tower and start a new character.

I've noticed among Grim Dawn players a sort of division, between players who enjoy leveling characters, and players who rush through leveling to focus on endgame stuff.  I think that (say) my past ACKS players also divided naturally into these two categories.  For some of them, domains were the game and leveling was just something you did to get there.  Other felts compelled to get domains just to keep up with the endgamers in terms of domain XP, but had no interest in domains as ends to themselves.

I think in a "MEANINGFUL CAMPAIGN" with very high individual-player autonomy, having a few players pursue the domain endgame is probably less disruptive for everyone else than in a high-cohesion tight-party game.  Particularly without rules for XP from domains.  And if domains are explicitly endgame content, and at that point you're already about capped-out on XP progression anyway, who cares if they give XP or not?  The passage of time that Gygax describes, where you're probably only passing a couple weeks of game-time per week of real-time, also seems likely to keep adventuring PCs at the center of the action, while PCs hoping to only do domain stuff will be stuck waiting a lot.

...  I wonder what the 1e DMG has to say about domains specifically?

Sunday, June 6, 2021

"A Meaningful Campaign"

I was thinking in the shower about that oft-quoted bit of Gygaxiana:

YOU CAN NOT HAVE A MEANINGFUL CAMPAIGN IF STRICT TIME RECORDS ARE NOT KEPT.

(all-caps his).

His detractors use it to make fun of him - look at this guy, taking strict timekeeping too seriously and getting mad enough to put it in all caps.  His adherents take it as dogma.

But I got to thinking about Boot Hill's perspective on campaigns, and started to wonder - maybe he meant a structure with much more autonomy for individual players than we typically think of in campaigns.  He's not talking about an "adventure path", obviously, since the quote is from the AD&D 1e DMG and Dragonlance was yet a twinkle in Weis and Hickman's eyes.  Less obviously, I think he's not even talking about the way OSR campaigns are usually run, where the party has a lot of autonomy but players are more or less bound together by it.  One example of this position from Dungeon of Signs - "Old style D&D is not a story about any one PC, it's a story about the adventuring party as a whole, or ultimately about a fictional world as a whole."

I got curious about the context around the Gygax quote, so I dug up my previously-unopened pdf of the 1e DMG and lo and behold, a paragraph after "YOU CANNOT HAVE...", we get:

For the sake of example, let us assume that you begin your campaign on Day 1 of the Year 1000. There are four player characters who begin initially, and they have adventures which last a total of 50 days — 6 days of actual adventuring and 44 days of resting and other activity. At this point in time two new players join the game, one of the original group decides to go to seek the advice of an oracle after hiring an elven henchman, and the remaining three “old boys” decide they will not go with the newcomers. So on Day 51 player A’s character is off on a journey, those of B, C, and D are resting on their laurels, and E and F enter the dungeon. The latter pair spend the better part of the day surviving, but do well enough to rest a couple of game days and return for another try on Day 54 — where they stumble upon the worst monster on the first level, surprise it, and manage to slay it and come out with a handsome treasure. You pack it in for the night. Four actual days later (and it is best to use 1 actual day = 1 game day when no play is happening), on Day 55, player characters B, C, and D enter the dungeon and find that the area they selected has already been cleaned out by player characters E and F. Had they come the day after the previous game session, game Day 52, and done the same thing, they would have found the monster and possibly gotten the goodies!

Some penalty must accrue to the non-active, but on the other hand, the over-active can not be given the world on a silver platter. Despite time differences, the activities of the newcomers to the campaign should be allowed to stand, as Destiny has decreed that the monster in question could not fall to the characters B, C, and D. Therefore, the creature was obviously elsewhere (not dead) when they visited its lair on Day 52, but it had returned on Day 56. Being aware of time differences between groups of player characters will enable you to prevent the BIG problems. You will know when the adventuring of one such group has gone far enough ahead in game time to call a halt. This is particularly true with regard to town/dungeon adventures.

 (emphasis mine)

Can you imagine the drama that would ensue if two new players joined your campaign (group?) and your existing players decided to not go adventuring with them?  I suspect that even in the vast majority of OSR campaigns today, this would be seen as a gross violation of social norms.  Even the West Marches assumes a cooperative community of PCs, a sort of "whoever's at the table that day goes adventuring together".  And yet here Gygax writes as if it were perfectly normal, as if association within the game-world was never taken for granted (and this example wasn't even one of those 20+ person campaigns mentioned in OD&D Book 1 - this is six players!).  This is what I mean by "no party" - there are player characters in the world and they interact with each other as they will.  Sometimes they work together to achieve their objectives, but that's a choice.  A party exists only for a single adventure.  Outside of an adventure, you can do as you please.  You want to go haring off after some oracle (for about a month, in the paragraph following the quoted one)?  By all means!  You want to spend a month just resting and healing?  Sure!  But you might get scooped on treasure.

It makes a lot of sense that if you have that norm, of players going off and doing their own things, and splitting into multiple parties, then yeah, you are going to want timekeeping!  As he says, to prevent "BIG" continuity problems.

The time lines of various player characters will diverge, meet, and diverge again over the course of game years. This makes for interesting campaigns and helps form the history of the milieu. Groups of players tend to segregate themselves for a time, some never returning to the ken of the rest, most eventually coming back to reform into different bands. As characters acquire henchmen, the better players will express a desire to operate some of theirs independently while they, or their liege lord, are away. This is a perfectly acceptable device, for it tends to even out characters and the game. Henchmen tend to become associates — or rivals — this way, although a few will remain as colorless servitors.

You may ask why time is so important if it causes such difficulties with record-keeping, dictates who can or can not go adventuring during a game session, and disperses player characters to the four winds by its strictures. Well, as initially pointed out, it is a necessary penalty imposed upon characters for certain activities [mostly magic item creation]. Beyond that, it also gives players yet another interesting set of choices and consequences. The latter tends to bring more true-to-life quality to the game, as some characters will use precious time to the utmost advantage, some will treat it lightly, and some will be constantly wasting it to their complete detriment. Time is yet another facet which helps to separate the superior players from the lesser ones. If time-keeping is a must from a penalty standpoint, it is also an interesting addition from the standpoint of running a campaign.

Emphasis again mine.  A couple of interesting things in these bits.  One is that the "diverge, meet, diverge again" is very much in the model of, say, Thieves' World, where there are persistent characters who make temporary alliances.  I have heard fiction in this form referred to as picaresque, but looking up the actual properties of picaresque I'm not so sure (I do like almost all of those in my D&D though).  The temporary nature of "bands" is again emphasized.  "interesting set of choices and consequences" is a very gamey thing to say, as is "separate the superior players from the lesser ones".  Gygax here is talking about D&D as a game that you can be better or worse at, and I think would not only say that it is acceptable for some players to fall behind as a result of bad choices and bad luck, but desirable.

So, returning to "meaningful campaign".  It seems that "campaign" here is meant much like the Boot Hill style of campaigning, a big set of interacting characters and a series of skirmish actions with a degree of continuity.  It seems that "meaningful" is meant in some combination of "maintaining internal consistency" and "preserving the agency of each individual player, that their choices about how to spend their resources [time] have consequences."

I'm really curious to see how this notion of great individual agency squares against the practice of having a caller.  I get the feeling I'm going to end up doing a lot more reading from the 1e DMG in the near future.  I found this a more thoughtful position on time, and better-articulated, than I expected.

Sunday, May 30, 2021

Entropy as a Character-Generation Currency

Had a conversation with my father today about character generation, random stats vs point buy, and Traveller character generation (including how death-in-chargen leads to intra-party balance in expectation more readily than allowing/expecting characters who fail survival rolls to be played in the company of those who passed all survival rolls).  While discussing point buy schemes and how it's sort of hard to put a number on the value of an 18, but that rolling dice has the problem of "auditability" (did they actually roll these stats?) I got to thinking...

Even if you don't want to actually obey dice, you can expect results that deviate from expectation to a certain degree, and that's a property that you can check.  Ability scores occur with certain probabilities.  Given a set of stats, one could compute the probability of that set occurring.  Depending on the sort of campaign one is running, one could establish bounds on the improbability of each set of chosen stats.

In information theory, there's a concept of "surprisal" in the occurrence of an event, which roughly quantifies how surprising it is given the probability of its occurrence (also called self-information).  If an event occurs with probability p, then its surprisal is -lg(p).  So given the probability of each ability score roll, we can compute the total surprisal of a set of stats.  And one nice property of logarithms of probability is that when you would multiply probabilities, adding their logarithms is equivalent (eg, 0.5 * 0.5 = 0.25.  lg(0.5) = -1, lg(0.25) = -2, so lg(0.5) + lg(0.5) = lg(0.25)).  Being able to work with them additively rather than multiplicatively is a desirable property for something like a point-buy system.

Stat% chanceProbabilitySelf-information (bits)Normalized self-informationScaled and rounded self-information (deci-bits)
30.460.00467.764.7648
41.390.01396.173.1732
52.780.02785.172.1722
64.630.04634.431.4314
76.940.06943.850.858
89.720.09723.360.364
911.570.11573.110.111
1012.50.125300
1112.50.125300
1211.570.11573.110.111
139.720.09723.360.364
146.940.06943.850.858
154.630.04634.431.4314
162.780.02785.172.1722
171.390.01396.173.1732
180.460.00467.764.7648

So we could use these scaled surprisal values as points during character generation.  But a set of all 10s and 11s is surprisingly unsurprising; an average set rolled on 3d6 looks more like 7, 9, 10, 11, 12, 14 than like all 10s and 11s.  If you wanted to model stat-lines at this level of surprise, a reasonable approach might be that you get a 7 in any one stat and 8 deci-bits to spend on the other 5, with the option to take a 9 to get a credit of 1 deci-bit.  Realistically, this means you get either a 14 or two 13s and the rest are 10s or 11s (unless you take the 9, which buys you a 12).  Might also want to add a rule that you should have close to the same number of 11s and 10s.

Honestly 13, 13, 11, 11, 10, 7 is a very playable set in B/Xy games.  I could absolutely see giving new players pregens with this array.

But going from there to higher-entropy statblocks seems sort of tricky.  If you let players take a 3 to buy an 18 (or a 6 and a 7 to buy a 16), their stats are "in balance", but more surprising /  less natural / less likely than a statblock with an 18 and a 10 would be!

Average stats of 4d6 drop 1 are more like 9, 10, 12, 13, 14, 16 - 34 deci-bits with the option to take a 9 for one more, I suppose?  Four 14s and a pair of 12s is nothing to scoff at in 3.x, while in B/X 16, 13, 13, 13, 11, 10 (or 12, 9) is a very solid set.

Perhaps it would make more sense to compute the probability (and then surprisal) of each ability score modifier band (per game-system), so that a 13 and a 14 are more-or-less equivalent?

Maybe the real problem here is that we're computing surprisal of each score in isolation, when maybe we should be computing the surprisal of the whole set.  Having an 18 as the highest score in a set isn't really that surprising - 6 stats, each with a 1-in-216 chance of being an 18, means a 1-in-36 chance that at least one is an 18, which is the same probability as having a 16 in any particular score.  But I'm not actually familiar enough with information theory to say if I would need something more complex like joint/mutual entropy (but it seems like there shouldn't be any mutual information between stats in a rolled character, because the stat rolls are independent, so you should just be able to add the self-informations together to get its aggregate information).  So I think this line of thought, evaluating the whole set of stats together, would take more thinking.

In any case, an aside - if we're considering using surprise as a currency in character generation, we could also use it to buy "weird stuff".  Want to play a lawful drow, or the lost son of the rightful king, or a balrog?  Fine, but those are extraordinarily rare and that costs entropy that you then aren't spending on your stats.  If elves are half as common among adventurers as humans in your setting, then being an elf is about 10 deci-bits of surprise.  And then maybe we can get rid of stat minimums for demi-humans (which currently impose roughly that effect - three-quarters of stat-lines qualify to be dwarves, and three-quarters qualify to be elves; call it 4 deci-bits).

Thursday, May 13, 2021

Chesterton on Letting the Dice Fall Where They May (but Unseriously)

Continuing with Orthodoxy (chapter 7):

I could never conceive or tolerate any Utopia which did not leave to me the liberty for which I chiefly care, the liberty to bind myself. Complete anarchy would not merely make it impossible to have any discipline or fidelity; it would also make it impossible to have any fun. To take an obvious instance, it would not be worth while to bet if a bet were not binding. The dissolution of all contracts would not only ruin morality but spoil sport. Now betting and such sports are only the stunted and twisted shapes of the original instinct of man for adventure and romance, of which much has been said in these pages. And the perils, rewards, punishments, and fulfilments of an adventure must be real, or the adventure is only a shifting and heartless nightmare. If I bet I must be made to pay, or there is no poetry in betting. If I challenge I must be made to fight, or there is no poetry in challenging. If I vow to be faithful I must be cursed when I am unfaithful, or there is no fun in vowing... For the purpose even of the wildest romance results must be real; results must be irrevocable.

which reminded me variously of illusionism (where the results aren't real), and storygames (where the players are authorially unbound), and of discussions of agency.

On the other hand,

Pride is the downward drag of all things into an easy solemnity. One "settles down" into a sort of selfish seriousness; but one has to rise to a gay self-forgetfulness... Seriousness is not a virtue. It would be a heresy, but a much more sensible heresy, to say that seriousness is a vice. It is really a natural trend or lapse into taking one's self gravely, because it is the easiest thing to do. It is much easier to write a good TIMES leading article than a good joke in PUNCH. For solemnity flows out of men naturally; but laughter is a leap. It is easy to be heavy: hard to be light.

which reminded me of this post of mine, where I concluded "Perhaps the problem with my previous approach to RPGs was taking things entirely too seriously."  And that is not something I have remedied, really.  It reminded me also of Lurkerablog's excellent post on tiki and early D&D:

Thinking about it, the slow evaporation of the Tiki mood from DnD just might be what defines the edge between James Malichewski’s Golden and Silver ages. When DnD got its visual style defined as heavy metal it acquired metal’s earnestness – the wargamer tourists of the 70s gave way to a new player base of DnD natives who took it all very seriously and wanted to know just how heavy that axe was. Kitsch, whimsy, a lack intensity – these became signs of poor commitment.

It is an easy error to make, for irrevocability to become serious, for it to turn to grave plotting to limit one's risks.  But I do think my favorite ACKS players have been the ones who took irrevocability in stride, for whom it was not a deterrent to action.  "Ha, told you we'd survive!" (or "that was a really funny death, it's going to be hard to top that")  I don't know how I would encourage such an attitude though.

Maybe part of the problem is that ACKS takes itself seriously.  That's part of why it's good; because it was taken seriously during its creation.  But it's not without its costs.

Thursday, April 29, 2021

Traveller: Why Are Radioactives Expensive?

Reflecting on Traveller and gross planetary product, I got to thinking about radioactives.  They're worth a million credits a ton, and it's a little puzzling.  What are radioactives used for in Traveller?  Nuclear weapons are purely the Imperium's prerogative, so that's pretty much out (but radioactives aren't illegal on their own, so it's also not like a black market price inflation sort of thing).  They're not being used for starship armor, probably (almost certainly not for crystal-iron or titanium steel.  Maybe for "bonded superdense"?  But that sounds more like neutronium than depleted uranium).  Is DU being used in infantry weapons and armor?  But you don't really need radioactives for DU, it's depleted.  It's probably not being used for medical imaging with all the higher-TL stuff available.  And it's not being used for power because fusion technology exists.

Fusion, incidentally, sounds like a decent way to synthesize radioactives, since that's how stars do it.  Horribly energy intensive, yes - but you have fusion power.  So fuse hydrogen for energy, and then use that energy to fuse lead or whatever to get your radioactives.

I've got half a mind to remove fusion power and make starships fission powered, as a means of explaining why anybody in Traveller gives a hoot about radioactives.  Doesn't matter how far in the future you go, fusion is still 10 years away.

But I don't think I'd want to use Mongoose's rules for fission power, which are pretty punitive.  I'm fine with the gameplay of the fusion reactor, just not the in-world implications.  Keep the same reactor volume and cost, keep the same fuel volume, but you only have to replace it once every, oh, ten years or so, and have the total cost of the replacement fuel rods add up to what you would've spent on refined hydrogen fuel for a typical fusion reactor over that time.  And then lift HOSTILE's hyperdrive and maneuver drive rules, you're heating hydrogen on the reactor and using that for thrust.

Monday, April 26, 2021

Traveller: How Big is the Militia of that Mining Colony?

(This is a "thinking out loud / showing my work" post)

Thinking about Boot Hill, Traveller, and (naturally) Starcraft led me to the question - how much military hardware and how many trained men does a backwater mining colony have?

Fortunately, Striker has rules for the GDP of planets based on their population, tech level, and economy tags, and suggestions about what fraction of that GDP is allocated to military spending (and ground vs spacy-navy spending) based on situation.

Let's take, say, the world of Serpentine from HOSTILE (subsector New Concession Zone, UWP D590355-C, Desert).  Population digit 3 means it has a few thousand people; applying Benford's Law and a d% roll, about 3000 people.  Per Striker, a TL12 Desert world has a per-capita GDP of 16kCr, so with 3k people total planetary GDP is 48 MCr.  Assuming 3% of GDP is spent on the military (Striker's baseline), that's 1.44 MCr/year.  60% (864 kCr) goes to the navy and 40% to the army (576kCr) (again, Striker's baseline for a world with an atmosphere).  

One place I'm diverging from Striker's assumptions is that 30% of defense spending goes to the Imperium.

That Navy budget is enough to afford a new police cutter (at MgT1e's prices) every, mmm...  65 years.  Once they have one, maintenance and fuel is about 120kCr/year.  A pilot is 72kCr/year salary, and a gunner is 24kCr/year, so TCO of a crewed cutter is 216 kCr/year.  Assuming the colony has been around a long time, their "navy" might field four such police cutters, and maybe 1-2 are on duty at any given time.  The limiting factor here might be human though - pilots have to sleep, machines don't.  If we went down to three cutters we could pick up an extra two pilots and three gunners (and maybe some admin staff) and that might improve availability somewhat but ultimately "between 1 and 3 police cutters on duty at any given time" is still going to be the right answer.

A solar system is a lot of space to cover with three cutters, at least one of which is probably off duty at any given time.  Pirates take note.

Meanwhile, on the surface, 576 kCr/year in army budget.  Government type 5 is the infamous Feudal Technocracy, which sounds like the sort of government that would field a mix of long-service feudal retainers and militia.  A long-service professional soldier costs 30kCr/year in wages, facilities, support personnel, etc, while a militiaman costs 10kCr/year.  So if we didn't have to buy or maintain any gear and were going just for number of bodies, the upper limit on the size of Serpentine's army would be (drumroll) 57 militia, about two platoons.  Which, to be fair, is about 2% of the population.  In times of crisis, with the military budget jacked up to 15% of GDP, they could support almost 300 militia, about two companies (10% of the population).

What gear do our infantry need?  Atmosphere type is 9, "Dense, Tainted", which means they'll all need filter masks.  Serpentine's temperature isn't listed in HOSTILE, but rolling it gave me Temperate, which is a bit odd for a desert world but whatever I'll allow it.  In any case, it seems like they don't need a great deal of protective equipment just to go outside.  Let's go with something like HOSTILE's ballistic vest (450Cr, 45Cr/year maintenance, AR5, 2kg) for armor.  Probably don't need more than one short-range radio per fireteam (250Cr each in HOSTILE), plus one medium or long-range radio for per platoon (1kCr in HOSTILE).  Assault rifles are on the order of 1-3 kCr each, depending on details.  Machine guns are in the same range.  So with equipment maintenance per year at 10% of its base price, we're looking at about an extra, say, 400 Cr/year in gear maintenance, which is peanuts next to personnel upkeep.

Without going through Striker's design sequences, we could consider picking up a couple of APCs at HOSTILE's prices; 100kCr to buy, 10kCr/year upkeep.  Crew of two, 13 passengers, means that four APCs would definitely cover us for the annual price of four militia.  Sounds like a reasonable deal to me, and helpful for moving them around in an unfriendly (though not outright deadly) environment.

So at the end of the day, neglecting the potential "feudal retainer professionals", we're looking at four APCs, 53 militia.  Eight of our militiamen are vehicle crew (four drivers, four gunners), leaving 49 infantry.  Maybe drop one more of the infantrymen and pick up a couple trucks or something in case one of the APCs is down for maintenance, and that also leaves us some buffer to buy a bit of new gear every year.  It is a little weird to give armored vehicles to militia, but it's a mining colony, they're operating and maintaining dump trucks and excavators daily anyway.

Or we could go up to professionals, and get one APC, 15 guys (two of whom are crew), and have a lot more slack to work with for replacing and upgrading gear (about 100 kCr/year - enough to replace the APC annually if necessary).

But the important thing here - this is a small enough army that PCs could conceivably go up against it, or make a difference against the sort of threats that it could deal with.  15-30 guys with assault rifles and an armored vehicle or two is a scary encounter in Traveller, but not impossible to deal with given command and control, morale, dispersion, defeat in detail, low skill levels on militia, and fighting dirty.  If you get the entire army of 50 militiamen and four APCs shooting at you at once, yeah, you're probably hosed.

But because Traveller's population codes go up exponentially, at Pop 4 we'd expect about 10x the population, 10x the GDP, and consequently 10x the army.  So that would be more like a couple of companies, and a much harder thing for PCs to deal with.  So I guess I got lucky picking the break point as my first testcase.  Meanwhile at population 2, which is 1/10th the GDP of Pop 3, you're looking at an "army" the size of the party.

In conclusion: Population 3 or less, maybe you can personally fight their army without having a military unit to back you up.  Population 4 or more, probably not.